70 research outputs found
Universal Time Scale for Thermalization in Two-dimensional Systems
The Fermi-Pasta-Ulam-Tsingou problem, i.e., the problem of energy
equipartition among normal modes in a weakly nonlinear lattice, is here studied
in two types of two-dimensional (2D) lattices, more precisely in lattices with
square cell and triangular cell. We apply the wave-turbulence approach to
describe the dynamics and find multi-wave resonances play a major role in the
transfer of energy among the normal modes. We show that, in general, the
thermalization time in 2D systems is inversely proportional to the squared
perturbation strength in the thermodynamic limit. Numerical simulations confirm
that the results are consistent with the theoretical prediction no matter
systems are translation-invariant or not. It leads to the conclusion that such
systems can always be thermalized by arbitrarily weak many-body interactions.
Moreover, the validity for disordered lattices implies that the localized
states are unstable.Comment: 6 pages, 4 figure
Thermal conductivity of the Toda lattice with conservative noise
We study the thermal conductivity of the one dimensional Toda lattice
perturbed by a stochastic dynamics preserving energy and momentum. The strength
of the stochastic noise is controlled by a parameter . We show that
heat transport is anomalous, and that the thermal conductivity diverges with
the length of the chain according to , with . In particular, the ballistic heat conduction of the
unperturbed Toda chain is destroyed. Besides, the exponent of the
divergence depends on
Wave Turbulence and thermalization in one-dimensional chains
One-dimensional chains are used as a fundamental model of condensed matter,
and have constituted the starting point for key developments in nonlinear
physics and complex systems. The pioneering work in this field was proposed by
Fermi, Pasta, Ulam and Tsingou in the 50s in Los Alamos. An intense and
fruitful mathematical and physical research followed during these last 70
years. Recently, a fresh look at the mechanisms of thermalization in such
systems has been provided through the lens of the Wave Turbulence approach. In
this review, we give a critical summary of the results obtained in this
framework. We also present a series of open problems and challenges that future
work needs to address.Comment: arXiv admin note: text overlap with arXiv:1811.05697 by other author
Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
This Chapter contains an overview of the effects of nonlinear interactions in
selected problems of non-equilibrium statistical mechanics. Most of the
emphasis is put on open setups, where energy is exchanged with the environment.
With reference to a few models of classical coupled anharmonic oscillators, we
review anomalous but general properties such as extremely slow relaxation
processes, or non-Fourier heat transport.Comment: Review paper, to appear in the volume "Nonlinear Science: a 20/20
vision", Springer Frontiers Collection (J. Cuevas, P. Kevrekidis and A.
Saxena Editors
Nonintegrability-driven Transition from Kinetics to Hydrodynamics
Nonintegrability plays a crucial role in thermalization and transport
processes in many-body Hamiltonian systems, yet its quantitative effects remain
unclear. To reveal the connection between the macroscopic relaxation properties
and the underlying dynamics, the one-dimensional diatomic hard-point model as
an illustrating example was studied analytically and numerically. We
demonstrate how the system transitions from kinetic behavior to hydrodynamic
behavior as the nonintegrability strength increases. Specifically, for the
thermalization dynamics, we find a power-law relationship between the
thermalization time and the perturbation strength near integrable regime,
whereas in the far from integrable regime, the hydrodynamics dominates and the
thermalization time becomes independent of the perturbation strength and
exhibits a strong size-dependent behavior. Regarding transport behavior, our
results further establish a threshold for the nonintegrable strength of this
transition. Consequently, we can predict which behavior dominates the transport
properties of the system. Especially, an explicit expression of the thermal
conductivity contributed by the kinetics is given. Finally, possible
applications were briefly discussed.Comment: 6 pages;5figure
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